mersenneforum.org > Math A non-linear differential equation
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 2010-07-08, 12:16 #1 Random Poster     Dec 2008 179 Posts A non-linear differential equation Consider the differential equation $y''y=nx^ny'$. Obviously $y=x^{n+1}$ is a solution, but are there any others?
 2010-07-08, 14:06 #2 wblipp     "William" May 2003 New Haven 3·787 Posts y=ax+b when n=0
 2010-07-18, 22:31 #3 ccorn     Apr 2010 9616 Posts y = const. for any n; and if $y=y_1(x)$ is a solution, then $y=\alpha^{-(n+1)}y_1(\alpha x)$ is a solution too, for arbitrary $\alpha$ from the field of x. This does not help generalizing the solutions given so far, however. Last fiddled with by ccorn on 2010-07-18 at 22:33

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